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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 8, Problem 45RE
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Solving a Trigonometric Equation In Exercises 45-50, solve the equation for θ . Assume 0   < θ < 2 π . For some of the equations, you should use the trigonometric identities listed in Section 8.2. Use a spreadsheet or a graphing utility to verify your results.

2 cos θ + 1 = 0

To determine

To calculate: The value of θ for the trigonometric equation, 2cosθ+1=0.

Explanation

Given Information:

The provided trigonometric equation is, 2cosθ+1=0.

Formula used:

The value of cosine function at π3 is,

cosπ3=12

Calculation:

Consider the trigonometric equation,

2cosθ+1=0

Solve the above trigonometric equation,

2cosθ+1=02cosθ=−1cosθ=−12

Since, cosπ3=12 and cosine is negative in second and third quadrants. Therefore, there are two solutions for trigonometric equation cosθ=−12, which can be mathematically determined as,

θ=π−π3=2π3=2.0943951

And,

θ=π+π3=4π3=4.1888790

The steps used to find the solution of the trigonometric function Y=2cosθ+1 within range of 0≤θ≤2π by the use of graphic calculator Ti-84, which can be given as below,

Step 1: Press ON button and then press Y= button.

Step 2: Then, enter the function Y=2cos(x)+1

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Sect-8.1 P-1CPSect-8.1 P-2CPSect-8.1 P-3CPSect-8.1 P-4CPSect-8.1 P-1SWUSect-8.1 P-2SWUSect-8.1 P-3SWUSect-8.1 P-4SWUSect-8.1 P-5SWUSect-8.1 P-6SWU
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BUSINESS DECISION: THE CONSULTATION 20. Tina Parker, a single mother, is 20 years old. She has called on you fo...

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Writing an Equation In Exercises 69-72, write an equation for the function having the given characteristics. Th...

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Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the curve. 1. x = t2 ...

Single Variable Calculus: Early Transcendentals

Prove the associative law for conjunction, (pq)rp(qr).

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Suppose that each of the bases of the triangular prism in Exercise 2 has an area of 3.4 in2 and that each later...

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Precalculus or Calculus In Exercises 3-6.decide whether the problem can be solved using precalculus or whether ...

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The area of the shaded region is given by:

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True or False: Partial fractions may be used for .

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Curvature Use the result of Exercise 69 to find the curvature of each polar curve. (a) r=1+sin (b) r= (c) r=asi...

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Write an equation in standard form of each of each ellipse described. Foci at (2,4) and (8,4); b=4

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If a=5.2,b=4.8,and c=7.25 ,what is the value of 2a2b+4cabc9a ? If necessary, round your answer to 3 decimal pla...

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For a within-subjects experiment, explain how the time delay between treatments can influence time-related thre...

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According to the National Oceanic and Atmospheric Administration (NOAA), the state ofColorado averages 18 torna...

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Sometimes samples are composed entirely of volunteer responders. Give a brief description of the dangers of usi...

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The purpose of an independent-measures t-test is to determine whether the mean difference obtained between two ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Consider a variation of the PDC decision tree shown in Figure 21.5. The company must first decide whether to un...

Statistics for Business & Economics, Revised (MindTap Course List)

Finding the Volume of a Solid In Exercises 3-12, use the shell method to write and evaluate the definite integr...

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